What is ln(x^9)-1/4 ln(x^{-7}) ?

The solution to ln(x^9)-1/4 ln(x^{-7}) is ln(x^{43/4})

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simplify ln(x^9)-1/4 ln(x^{-7})

simplify

ln (x^{9}) - \frac{1}{4} ln (x^{- 7})

ln (x^{\frac{43}{4}})

Solution steps

ln (x^{9}) - \frac{1}{4} ln (x^{- 7})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{4} ln (x^{- 7}) = ln ((x^{- 7})^{\frac{1}{4}})

= ln (x^{9}) - ln ((x^{- 7})^{\frac{1}{4}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{9}) - ln ((x^{- 7})^{\frac{1}{4}}) = ln (\frac{x ^{9}}{( x ^{- 7} ) ^{\frac{1}{4}}})

= ln (\frac{x ^{9}}{( x ^{- 7} ) ^{\frac{1}{4}}})

Simplify

\frac{x ^{9}}{( x ^{- 7} ) ^{\frac{1}{4}}} : x^{\frac{43}{4}}

= ln (x^{\frac{43}{4}})

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lo g_{4} (\frac{2 x + 1}{3 y + 4})

\frac{1}{2} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

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lo g_{8} (\frac{3 x ^{3}}{( 4 ) ( 3 )})

What is ln(x^9)-1/4 ln(x^{-7}) ?
The solution to ln(x^9)-1/4 ln(x^{-7}) is ln(x^{43/4})